Resuming at 193-2, Smith and Khawaja extended their partnership to 188 runs before Moeen Ali got the prize breakthrough of Smith moments before lunch, to leave the hosts 69 runs behind England's first-innings total of 346.
At lunch today, Khawaja was 132 not out, with Shaun Marsh unbeaten on two.
Khawaja's sixth Test century was timely given the 31- year-old hadn't scored a hundred since his 145 against South Africa in Adelaide in November 2016, and questions around his spot in the team had begun to arise after only scoring two 50s in six innings this series.
A clearly relieved Khawaja celebrated by removing his helmet and raising his bat toward his teammates and family seated in the Members Stand at the SCG, before being warmly embraced by Smith.
At the other end, Smith continued to frustrate England as he relentlessly closed in on another century and matching Bradman's 1930 feat of scoring four tons in an Ashes series.
Debutant legspinner Mason Crane thought he had his first test wicket in the last over before lunch, but his review for an lbw on Khawaja showed the bowler had overstepped for a no- ball. To Crane's dismay, replays showed the ball would have hit the stumps and the review would have been successful had he not overstepped.
England still face the likelihood of a first-innings deficit, despite a strong rally on Friday morning by their lower order which lifted the tourists to a competitive 346, after it had slumped to 233-5 when it lost its last specialist batsman, Dawid Malan (62), early in the session.
Australia won the first three tests convincingly to regain the Ashes, and the fourth test was drawn last week in Melbourne.
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